Given
[tex]\begin{gathered} f(x)=(x+10)^{\frac{1}{2}} \\ \\ g(x)=(x+10)^{\frac{1}{3}} \end{gathered}[/tex]
Find
Domain of the function
Explanation
Domain of the function is the set of all possible values of x which will given the output value y.
[tex]\begin{gathered} f(x)=\sqrt{(x+10)} \\ x+10=0 \\ x=-10 \end{gathered}[/tex]
so , domain of the function , f(x) =
[tex][-10,\infty)[/tex]
and
as we know that the domain of the function is all real numbers except where the function is undefined.
in this case , there is no real number which makes the function undefined.
so , domain of g(x) is all values of x
so ,
[tex]g(x)=(-\infty,\infty)[/tex]
Final Answer
Therefore , the domain of f(x) anf g(x) are
[tex]f(x)=[-10,\infty)[/tex][tex]g(x)=(-\infty,\infty)[/tex]
